An oil heat exchanger in which lubricant oil of an automatic transmission flows is specially provided in a conventional cooling water circuit in which engine-cooling water flows when a thermostat is closed (e.g., JP-A-2002-47935). The heat exchanger performs heat exchange between the lubricant oil and engine-cooling water, so as to heat the lubricant oil in a warming-up operation after the vehicle engine starts, and to cool the lubricant oil in an engine normal operation. However, in this heat exchanger, because the lubricant oil is heated by using cooling water (hot water) in a heater water circuit to sufficiently heat the lubricant oil in the warming-up operation, the lubricant oil may be not sufficiently cooled in the engine normal operation sometimes. Conversely, when cooling water after passing through a radiator is used in the heat exchanger for sufficiently cooling the lubricant oil, warming-up performance of the lubricant oil after the engine start may be deteriorated.